Scheduling parallel machines with inclusive processing set restrictions

Abstract

Abstract:We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst-case performance ratio of 4 3 + , where is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature.

Multiple subset sum with inclusive assignment set restrictions

“…Counting the number of ms-items packed by the optimal algorithm, we have β 01 + β 11 + 2β 02 + β 01 + β 11 + 2β 02 ≤ α 11 + 2α 02 + γ , which implies that β 11 + β 02 ≤ α 11 + 2α 02 − β 01 − β 11 − 2β 02 + γ . By (13), this inequality becomes…”

“…A typical machine scheduling model with this kind of assignment restriction appears in parallel machine models, where some machines are more flexible and can process more jobs, while other machines are less flexible and can process fewer jobs. For example, Ou et al [13] have studied such a scheduling problem with "inclusive processing sets," while Huo and Leung [14] and Muratore et al [15] have studied a more general model with "nested processing sets." Leung and Li [16] have provided a comprehensive survey of scheduling models with job assignment restrictions in general and inclusive/nested processing set restrictions in particular.…”

Makespan minimization in online scheduling with machine eligibility

“…In manufacturing and logistics industry, Glass and Mills (2006) describe an application of nested processing in the drying stage of a flour mill in the United Kingdom and Ou et al (2008) consider cranes with weight limit for loading and unloading cargoes of a vessel and find that crane restriction of handling each piece of cargo can be modelled into GoS eligibility constraints. In service provision application, Hwang et al (2004b) present a differentiation scheme for different grade of service level customers and Wang and Xing (2010) analyze the worst-case performance for various on-line service polices.…”

Scheduling parallel machines with inclusive processing set restrictions and job release times

“…A strongly polynomial time approximation algorithm can be obtained by modifying A2 slightly using the method presented in [23]. First, as mentioned in Remark 1, we can use algorithm A1 to obtain a 3-approximation solution to problem P | r j , incl.…”

“…proc. sets | C max with a constant bound on the relative error is to apply the method developed by Ou et al [23]. Such an approach is described as follows:…”